The sign of the quadratic polynomial ax^2 + bx + c is always

• Quant Quadratic

The sign of the quadratic polynomial ax² + bx + c is always positive if

1. a is positive and b² - 4ac ≤ 0.
2. a can be any real number and b² - 4ac ≤ 0.
3. a can be any real number and b² - 4ac ≥ 0.
4. a is positive and b² - 4ac ≥ 0.

Answer

ax² + bx + c is always positive if there exists no real root and a is positive. This means the graph of the given polynomial will never cut the x-axis and will always lie above it.

The condition for no real root is b² - 4ac < 0. 

If we include the strict inequality i.e. b² - 4ac ≤ 0 (which is at most one real root), then it means the polynomial will always remain positive but can also take the value 0.

So, the answer is: a is positive and b² - 4ac ≤ 0.

On the other hand, if a is negative and b² - 4ac ≤ 0 holds, then the polynomial is always ≤ 0.

The correct option is A.